Find x for ln x=-2 using the natural logarithm formula

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Homework Help Overview

The discussion revolves around solving the equation ln x = -2, focusing on the implications of using the natural logarithm and its properties.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between natural logarithms and exponential functions, questioning whether x can be expressed as e^(-2). There is also a concern about the implications of negative values in logarithmic functions and whether a more complex approach is necessary.

Discussion Status

Some participants have provided insights into the relationship between ln x and e^(-2), while others have raised questions about the validity of using this approach for negative logarithmic values. The discussion reflects a mix of interpretations regarding the domain of the natural logarithm.

Contextual Notes

There is mention of the domain restrictions of the natural logarithm function, noting that it applies only to positive real numbers, which raises questions about the treatment of negative inputs.

justin345
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lnx=-2 ---- find x

Homework Statement



Hi!
We know that ln x=y, thus x=e^(y).
If I have ln x=-2, can my x be equal e^(-2)=0.135?
 
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justin345 said:

Homework Statement



Hi!
We know that ln x=y, thus x=e^(y).
If I have ln x=-2, can my x be equal e^(-2)=0.135?
Yes, ln x = -2 <==> x = e-2, which is approximately 0.135.
 


I am asking because for negative natural logs, there is a more complicated formula with sin and cos and Pi.
So you are saying that it is okay to use this one? Thank you!
 


No, I'm not saying that at all. For the real number version of the ln function, the domain is positive real numbers, and the range is all real numbers.

If you had ln(-2), that would be a different matter altogether, and you would need the complex version of this function.
 

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